Standardizability of linear periodic sampled-data systems

Abstract

Due to periodic sampling, linear sampled-data system are a subclass of linear continuous periodic systems, even in the case, when all other elements are time invariant. Owing to the great practical importance of sampled-data control systems, various approaches for the rigorous description of those systems are known. Moreover, a lot of methods have been developed, that are able to yield rigorous solutions for numerous control and optimization problems. The application of those methods need representations in certain standard forms. Often, it is not clear, whether a given system can be transformed into a standard form or not. The paper considers this question for the standard sampled-data system, for which numerous methods and tools are available, if the system belongs to the subclass with model structure. The paper provides necessary and sufficient conditions for a SD system with standard structure to belong to this important subclass. At hand of a simple SD system, it is shown that the standard structure does not imply model standardizability.